Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise

• URL: http://arxiv.org/abs/2301.03393v4
• Date: Fri, 16 Jun 2023 09:25:24 GMT
• Title: Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise
• Authors: Kevin Bui, Yifei Lou, Fredrick Park, Jack Xin
• Abstract summary: We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds awise-smooth solution, followed by $k-means to segment the image. Specifically for the image smoothing step, we replace the maximum noise in the MumfordShah model with a maximum variation of anisotropic total variation (AITV) as a regularization. Convergence analysis is provided to validate the efficacy of the scheme.
• Score: 2.6381163133447836
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by $k$-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

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